Abstract

Propagation of electromagnetic waves in a one-dimensional photonic crystal with a twin-defect—a periodicity break where one half of the photonic structure is a mirror image of the other one—is studied using a transfer-matrix method. This work is done in the general framework of photonic structures composed of isotropic materials exhibiting both dielectric and magnetic properties. Both polarizations of electromagnetic waves impinging at oblique incidence on the structure are considered. We derive analytical expressions for the frequency of defect modes and for the enhancement of the electromagnetic field inside the defect. In particular, we discuss possibilities of tuning of defect levels for a photonic crystal structure with a two-layer elementary cell.

(a) Dimensionless frequency [in units of c/(2ltot);ltot=nFdF+nLdL] of defect modes, (b) their relative tunability by optical thickness, and (c) enhancement of the electric field in the middle of the defect versus optical thickness of the defect. Dashed lines in (a) indicate band edges; thicker curves, even-parity modes; and thinner curves, odd-parity modes. The calculations were made with θ=0° and ZD=0.0025 (dotted curves), ZD=0.25 (solid curves), and ZD=25 (dashed–dotted curves). Parameters of the PC are nFdF=nLdL=ltot/2,ZF=1/3.4, and ZL=ZA=1. The number of periods in (c) is N=10. For clarity, only modes with m=2 are plotted in (b) and (c).

(a) Dimensionless frequency of defect modes and (b) their relative tunability by impedance versus impedance of the defect. Long-dashed lines-indicate band edges; Dashed–dotted curve, middle of the gap; dotted curve, asymptotic limits of defect levels when ZD→ 0 (m=2) or ZD→∞(m=3). The calculations were performed with nDdD=1.824ltot and θ=0°; other parameters are the same as in Fig. 3.

Dimensionless frequency of a defect mode as a function of angle of incidence θ on the PC. Dashed curves, band edges; dotted and solid curves, nDdD=0.735ltot and nDdD=ltot, respectively. For both polarizations ZD=0.25 and nA=1. Other parameters are the same as in Fig. 3.